¡Buen provecho! It is an expression of courtesy that Hispanics use at meal times with the intention of being nice to whoever is eating.

This expression can be used in three ways:

1. When we enter a place and we see people eating and we pass near them, we say ¡Buen provecho!
2. When we´re going to eat with other people, we say ¡Buen provecho! when we start eating.
3. When we finish eating and get up from the table, we say ¡Buen Provecho! and the other people reply ¡Gracias igualmente!

NOTE:
This is not grammar, it is culture. It is up to you whether you want to be polite or not.